Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
import sys
from operator import itemgetter

inf = 100500

def readints():
    return map(int, sys.stdin.readline().split())

def destroy_one_row(a, idx, val, res):
    if val > 0:
        res.append((val, "row {}".format(idx + 1)))
        for i in xrange(len(a[idx])):
            a[idx][i] -= val


def destroy_one_col(a, idx, val, res):
    if val > 0:
        res.append((val, "col {}".format(idx + 1)))
        for i in xrange(len(a)):
            a[i][idx] -= val


a = []
n, m = readints()
for i in xrange(n):
    a.append(readints())


def calcmins():
    min_rows = [inf] * n
    min_cols = [inf] * m
    for i in xrange(n):
        for j in xrange(m):
            min_rows[i] = min(min_rows[i], a[i][j])
            min_cols[j] = min(min_cols[j], a[i][j])

    return min_rows, min_cols

def destroy_cols(res):
    _, min_cols = calcmins()
    for i, val in enumerate(min_cols):
        destroy_one_col(a, i, val, res)

def destroy_rows(res):
    min_rows, _ = calcmins()
    for i, val in enumerate(min_rows):
        destroy_one_row(a, i, val, res)

res = []
if n < m:
    destroy_rows(res)
    destroy_cols(res)
else:
    destroy_cols(res)
    destroy_rows(res)

if all(all(elem == 0 for elem in row) for row in a):
    print sum(map(itemgetter(0), res))
    for cnt, move in res:
        for i in xrange(cnt):
            print move
else:
    print -1